Question

It x and y vary inversely, fill in the following blank:

x	16	32	8	128
y	4	...	...	0.25

Answer 1

\[ \text{ Since x and y vary inversely, we have } : \]
\[xy = k\]
\[\text{ For x = 16 and y = 4, we have: }  \]
\[16 \times 4 = k\]
\[ \Rightarrow k = 64\]
\[ \text{ For x = 32 and k = 64, we have:}  \]
\[xy = k\]
\[ \Rightarrow 32y = 64\]
\[ \Rightarrow y = \frac{64}{32}\]
\[ = 2\]
\[ \text{ For x = 8 and k = 64 } \]
\[xy = k\]
\[ \Rightarrow 8y = 64\]
\[ \Rightarrow y = \frac{64}{8}\]
\[ = 8\]